We construct a series of n-unimodal approximations to maps of the Hénon type and utilize the associated symbolic dynamics to describe the possible bifurcation structures for such maps. We construct the bifurcation surfaces of the short periodic orbits in the topological parameter space and check numerically that the Hénon map parameter plane (a,b) is topologically equivalent to a two-dimensional section through the infinite-dimensional parameter space characterizing a generic map of the Hénon type.